Probability Distribution Function Estimation for Tunnel Propagation via the Multilevel Monte Carlo Method

Accurate radio wave propagation modeling in tunnels is crucial to designing reliable wireless communication systems. Among the available techniques, the parabolic wave equation (PWE) methods have been widely utilized, due to their balance of accuracy and efficiency. However, estimating the full probability density function (PDF) of received power under uncertain tunnel and system parameters can be prohibitively expensive with standard Monte Carlo PWE (MC–PWE). Recently, the multilevel Monte Carlo PWE (MLMC–PWE) method has been proposed, which has shown excellent performance in the estimation of statistics of the received power along the tunnel. In this paper, we enhance the MLMC-PWE method by coupling it with kernel density estimation (KDE) to estimate the probability density function (PDF) of the received power. Compared with the Monte Carlo PWE (MC-PWE) method, the MLMC-PWE method can provide accurate estimations with low computational cost. In addition, compared with the polynomial chaos expansion, the proposed method obtains a higher accuracy with lower computational cost.